Zusammenfassung
Wir beweisen, dass sich lineare Gleichungssysteme (mit Gauß-Elimination) und lineare Programme (mit der Ellipsoidmethode) in polynomieller Zeit lösen lassen.
Wir gehen auch auf die Äquivalenz von Separation und Optimierung ein.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literatur
Allgemeine Literatur:
Grötschel, M., Lovász, L., und Schrijver, A. [1988]: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin 1988
Padberg, M. [1999]: Linear Optimization and Extensions. 2. Aufl. Springer, Berlin 1999
Schrijver, A. [1986]: Theory of Linear and Integer Programming. Wiley, Chichester 1986
Zitierte Literatur:
Bland, R.G., Goldfarb, D., und Todd, M.J. [1981]: The ellipsoid method: a survey. Operations Research 29 (1981), 1039–1091
Edmonds, J. [1967]: Systems of distinct representatives and linear algebra. Journal of Research of the National Bureau of Standards B 71 (1967), 241–245
Frank, A., und Tardos, É. [1987]: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7 (1987), 49–65
Gács, P., und Lovász, L. [1981]: Khachiyan’s algorithm for linear programming. Mathematical Programming Study 14 (1981), 61–68
Grötschel, M., Lovász, L., und Schrijver, A. [1981]: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (1981), 169–197
Iudin, D.B., und Nemirovskii, A.S. [1976]: Informational complexity and effective methods of solution for convex extremal problems. Ekonomika i Matematicheskie Metody 12 (1976), 357–369 [auf Russisch]
Karmarkar, N. [1984]: A new polynomial-time algorithm for linear programming. Combinatorica 4 (1984), 373–395
Karp, R.M., und Papadimitriou, C.H. [1982]: On linear characterizations of combinatorial optimization problems. SIAM Journal on Computing 11 (1982), 620–632
Khachiyan, L.G. [1979]: A polynomial algorithm in linear programming [auf Russisch]. Doklady Akademii Nauk SSSR 244 (1979) 1093–1096. English translation: Soviet Mathematics Doklady 20 (1979), 191–194
Khintchine, A. [1956]: Kettenbrüche. Teubner, Leipzig 1956
Lee, Y.T., und Sidford, A. [2014]: Path finding methods for linear programming. Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (2014), 424–433
Padberg, M.W., und Rao, M.R. [1981]: The Russian method for linear programming III: Bounded integer programming. Research Report 81-39, New York University 1981
Shor, N.Z. [1977]: Cut-off method with space extension in convex programming problems. Cybernetics 13 (1977), 94–96
Steinitz, E. [1922]: Polyeder und Raumeinteilungen. Enzyklopädie der Mathematischen Wissenschaften, Band 3 (1922), 1–139
Tardos, É. [1986]: A strongly polynomial algorithm to solve combinatorial linear programs. Operations Research 34 (1986), 250–256
Vaidya, P.M. [1996]: A new algorithm for minimizing convex functions over convex sets. Mathematical Programming 73 (1996), 291–341
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature
About this chapter
Cite this chapter
Korte, B., Vygen, J. (2018). Algorithmen für lineare Optimierung. In: Kombinatorische Optimierung. Masterclass. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57691-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-57691-5_4
Published:
Publisher Name: Springer Spektrum, Berlin, Heidelberg
Print ISBN: 978-3-662-57690-8
Online ISBN: 978-3-662-57691-5
eBook Packages: Life Science and Basic Disciplines (German Language)